Assume for a particular computer, the probability of failing due to a hard drive

Question

Assume for a particular computer, the probability of failing due to a hard drive error is 0.30, and the probability of failing to both a hard drive and motherboard error is 0.25. Assume failing from a hard drive error and motherboard error are independent.

(a) Find the probability that the computer fails due to a motherboard error.

(b) Find the probability the computer fails due to a motherboard error, but not a hard drive error.

(c) Find the probability the computer does not fail due to either error.

(d) Find the probability the computer fails to either one of the errors (or both).

(e) Find the probability that the computer fails due to a hard drive error, but not a motherboard error.

Explanation / Answer

Answer

Given event is independent

Probability of computer fails due to hard drive error P(H) = 0.3

Probability of computer fails due to hard drive and motherboard error P(H) * P(M) = 0.25

a) Probability that the computer fails due to motherboard error

P(M)      = 0.25 / 0.30

= 0.83

b) Probability that the computer fails due to motherboard error but not a hard drive error

P(M) – P(HM)    = 0.83 – 0.25

= 0.58

c) Probability that the computer does not fail due to either error

1 – (P(H) + P(M) – P(HM)) = 1 – (0.3 +0.83 – 0.25)

= 0.12

d) Probability that the computer fails due to one of the error (or both)

P(H) + P(M) – P(HM) = 0.3 + 0.83 – 0.25

= 0.88

e) Probability that the computer does not fail due to hard drive error, but not a motherboard error

P(H) – (PHM)     = 0.30 – 0.25

= 0.05

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